Question

LCM of 9, 12 and 15 is?

• A. 90
• B. 180
• C. 60
• D. 45

Hint:

To find the LCM, use the highest powers of all primes appearing in the factorizations of the numbers.

Answer 1

The Correct Option is B

To find the least common multiple (LCM) of 9, 12, and 15, we first find the prime factorizations of the numbers:
- \( 9 = 3^2 \)
- \( 12 = 2^2 \times 3 \)
- \( 15 = 3 \times 5 \)
Step 1: LCM Calculation
The LCM is obtained by taking the highest power of each prime that appears in the factorizations:
- For \( 2 \), the highest power is \( 2^2 \) (from 12)
- For \( 3 \), the highest power is \( 3^2 \) (from 9)
- For \( 5 \), the highest power is \( 5 \) (from 15)
Thus, the LCM is:
\[ \text{LCM} = 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180 \] Thus, the LCM of 9, 12, and 15 is \( 180 \).